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Additionally, there are several notions of randomness which are weaker than Martin-Löf randomness. Some of these are weak 1-randomness, Schnorr randomness, computable randomness, partial computable randomness. Yongge Wang showed cite-ref-11[11] that Schnorr randomness is different from computable randomness. Additionally, Kolmogorov–Loveland randomness is known to be no stronger than Martin-Löf randomness, but it is not known whether it is actually weaker.

At the opposite end of the randomness spectrum there is the notion of a K-trivial set. These sets are anti-random in that all initial segment is logarithmically compressible (i.e., K ( w ) ≤ ≤ K ( | w | ) + b {\displaystyle K(w)\leq K(|w|)+b} for each initial segment w), but they are not computable.

• Random sequence

• Gregory Chaitin

• Stochastics

• Monte Carlo method

• K-trivial set

• Universality probability

• Statistical randomness

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